Skip to content

Complex Simplify

Core to working with algebra problems is the ability to simplify complex terms, and Mathy provides an environment that generates problems with complex terms that require simplification to satisfy the win-conditions.

Challenge

In Complex Simplify the agent must learn to quickly combine coefficients and like variables inside a single complex term

Examples

  • 1x * 2x^1 must be simplified to 2x^2
  • 7j * y^1 * y^2 must be simplified to 7j * y^3

Win Conditions

A problem is considered solved when there are no remaining complex terms in the expression.

No Complex Terms

Terms are considered complex when there's a more concise way they could be expressed.

Examples

  • 2 * 4x is complex because it has multiple coefficients which could be simplified to 8x
  • 4x * y * j^2 is not complex despite being verbose because there is only a single coefficient and no matching variables

Example Episode

A trained agent learns to combine multiple low-level actions into higher-level ones that simplify complex terms

Input

4a^4 * 5a^4 * 2b^4

4 a 4 ^ * 5 a 4 ^ * 2 b 4 ^ * * *

Steps

Step Text
initial 4a^4 * 5a^4 * 2b^4
constant arithmetic 20a^4 * a^4 * 2b^4
variable multiplication 20 * a^(4 + 4) * 2b^4
constant arithmetic 20 * a^8 * 2b^4
commutative swap (a^8 * 2b^4) * 20
commutative swap (2b^4 * a^8) * 20
commutative swap 20 * 2b^4 * a^8
constant arithmetic 40b^4 * a^8
solution 40b^4 * a^8

Solution

40b^4 * a^8

40 b 4 ^ * a 8 ^ *


Last update: November 28, 2019